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010   $a981-15-6975-4
024 7 $a10.1007/978-981-15-6975-3
035   $a(CKB)4100000011354894
035   $a(DE-He213)978-981-15-6975-3
035   $a(MiAaPQ)EBC6272274
035   $a(PPN)258305088
035   $a(EXLCZ)994100000011354894
100   $a20200717d2020      u|             0
101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aStatistics Based on Dirichlet Processes and Related Topics$b[electronic resource] /$fby Hajime Yamato
205   $a1st ed. 2020.
210  1$aSingapore :$cSpringer Singapore :$cImprint: Springer,$d2020.
215   $a1 online resource (VIII, 74 p. 7 illus.) 
225 1 $aJSS Research Series in Statistics,$x2364-0057
300   $aIncludes index.
311   $a981-15-6974-6 
327   $aIntroduction -- Dirichlet process and Chinese restaurant process -- Nonparametric estimation of estimable parameter -- Random partition of positive integer.
330   $aThis book focuses on the properties associated with the Dirichlet process, describing its use a priori for nonparametric inference and the Bayes estimate to obtain limits for the estimable parameter. It presents the limits and the well-known U- and V-statistics as a convex combination of U-statistics, and by investigating this convex combination, it demonstrates these three statistics. Next, the book notes that the Dirichlet process gives the discrete distribution with probability one, even if the parameter of the process is continuous. Therefore, there are duplications among the sample from the distribution, which are discussed. Because sampling from the Dirichlet process is described sequentially, it can be described equivalently by the Chinese restaurant process. Using this process, the Donnelly?Tavaré?Griffiths formulas I and II are obtained, both of which give the Ewens? sampling formula. The book then shows the convergence and approximation of the distribution for its number of distinct components. Lastly, it explains the interesting properties of the Griffiths?Engen?McCloskey distribution, which is related to the Dirichlet process and the Ewens? sampling formula.
410  0$aJSS Research Series in Statistics,$x2364-0057
606   $aStatistics 
606   $aProbabilities
606   $aApplied mathematics
606   $aEngineering mathematics
606   $aApplied Statistics$3https://scigraph.springernature.com/ontologies/product-market-codes/S17000
606   $aStatistical Theory and Methods$3https://scigraph.springernature.com/ontologies/product-market-codes/S11001
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aApplications of Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M13003
615  0$aStatistics .
615  0$aProbabilities.
615  0$aApplied mathematics.
615  0$aEngineering mathematics.
615 14$aApplied Statistics.
615 24$aStatistical Theory and Methods.
615 24$aProbability Theory and Stochastic Processes.
615 24$aApplications of Mathematics.
676   $a331.257094
700   $aYamato$b Hajime$4aut$4http://id.loc.gov/vocabulary/relators/aut$01017965
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a996418252903316
996   $aStatistics Based on Dirichlet Processes and Related Topics$92391166
997   $aUNISA